Fourier coefficients of invariant random fields on homogeneous spaces of compact groups

Paolo Baldi; Stefano Trapani

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arXiv · 1304.5142

Fourier coefficients of invariant random fields on homogeneous spaces of compact groups

Paolo Baldi·Stefano Trapani

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Abstract

Let $T$ be a random field invariant under the action of a compact group $G$. In the line of previous work we investigate properties of the Fourier coefficients as orthogonality and Gaussianity. In particular we give conditions ensuring that independence of the random Fourier coefficients implies Gaussianity. As a consequence, in general, it is not possible to simulate a non-Gaussian invariant random field through its Fourier expansion using independent coefficients.

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Paolo Baldi, Stefano Trapani. 2013-04-18. Fourier coefficients of invariant random fields on homogeneous spaces of compact groups. https://arxiv.org/abs/1304.5142

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